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  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a4cb1cd3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# %matplotlib inline  #使用python 的matplotlib包来画图\n",
    "import random \n",
    "import torch \n",
    "from d2l import torch as d2l\n",
    "\n",
    "def synthetic_data(w, b, num_examples):\n",
    "    '''生成y  = x2 + b + 噪声'''\n",
    "    x = torch.normal(0, 1, (num_examples, len(w)))\n",
    "    y = torch.matmul(x, w) + b #矩阵乘法，多维时会有广播机制更复杂\n",
    "    y += torch.normal(0, 0.01, y.shape)\n",
    "    return x, y.reshape((-1, 1))\n",
    "\n",
    "true_w = torch.tensor([2, -3.4])\n",
    "true_b = 4.2\n",
    "features, labels = synthetic_data(true_w, true_b, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "511a9d3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feature: tensor([-1.1935,  0.2426]) \n",
      "label: tensor([0.9902])\n"
     ]
    }
   ],
   "source": [
    "print('feature:', features[0], '\\nlabel:', labels[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0083512e",
   "metadata": {},
   "outputs": [
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   "source": [
    "d2l.set_figsize()\n",
    "d2l.plt.scatter(features[:, 1].detach().numpy(),\n",
    "                labels.detach().numpy(),1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5905b49e",
   "metadata": {},
   "outputs": [],
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    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        batch_indices = torch.tensor(\n",
    "            indices[i:min(i + batch_size, num_examples)])\n",
    "        yield features[batch_indices], labels[batch_indices]\n",
    "batch_size = 10"
   ]
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  {
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   "execution_count": 5,
   "id": "2b162844",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-1.1935,  0.2426],\n",
      "        [-1.9982, -0.3925],\n",
      "        [ 1.2111, -1.0458],\n",
      "        [ 0.4384, -0.1674],\n",
      "        [-0.2887, -1.3295],\n",
      "        [-0.6267,  1.2228],\n",
      "        [ 0.8283,  0.9883],\n",
      "        [-0.0310, -0.8252],\n",
      "        [-1.3494,  1.2284],\n",
      "        [ 2.0479,  0.5960]]) \n",
      " tensor([[ 0.9902],\n",
      "        [ 1.5438],\n",
      "        [10.1790],\n",
      "        [ 5.6585],\n",
      "        [ 8.1288],\n",
      "        [-1.2025],\n",
      "        [ 2.4957],\n",
      "        [ 6.9451],\n",
      "        [-2.6804],\n",
      "        [ 6.2604]])\n"
     ]
    }
   ],
   "source": [
    "for x, y in data_iter(batch_size, features, labels):\n",
    "    print(x, '\\n', y)\n",
    "    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "133c0886",
   "metadata": {},
   "outputs": [],
   "source": [
    "w = torch.normal(0, 0.01, size= (2,1), requires_grad=True)\n",
    "b = torch.zeros(1, requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "39e93cd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linreg(x, w, b):\n",
    "    \"\"\"线性回归\"\"\"\n",
    "    return torch.matmul(x, w) + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fd865ab0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def squard_loss(y_hat, y):\n",
    "    \"\"\"均方损失\"\"\"\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 /2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "31691643",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size):\n",
    "    \"\"\"小批量随机梯度下降\"\"\"\n",
    "    with torch.no_grad(): #让参数计算不会自动求导\n",
    "        for param in params:\n",
    "            param -= lr * param.grad / batch_size\n",
    "            param.grad.zero_() #清空梯度，不然下次求导梯度会累加"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4b38e95c",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 0.03\n",
    "num_epochs = 3\n",
    "net = linreg\n",
    "loss = squard_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c16c71f8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1， loss 0.039835\n",
      "epoch 2， loss 0.000170\n",
      "epoch 3， loss 0.000049\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(num_epochs):\n",
    "    for x, y in data_iter(batch_size, features, labels):\n",
    "        l = loss(net(x,w,b), y)\n",
    "        l.sum().backward()\n",
    "        sgd([w,b], lr, batch_size)\n",
    "            \n",
    "    with torch.no_grad():\n",
    "        train_l = loss(net(features, w, b), labels)\n",
    "        print(f\"epoch {epoch + 1}， loss {float(train_l.mean()):f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "90d97d5a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w的误差： tensor([-0.0012, -0.0005], grad_fn=<SubBackward0>)\n",
      "b的误差: tensor([0.0007], grad_fn=<RsubBackward1>)\n"
     ]
    }
   ],
   "source": [
    "print(f'w的误差： {true_w - w.reshape(true_w.shape)}')\n",
    "print(f'b的误差: {true_b - b}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c29ae4a8",
   "metadata": {},
   "source": [
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   "cell_type": "code",
   "execution_count": null,
   "id": "488fe936",
   "metadata": {},
   "outputs": [],
   "source": []
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